1. understood that symbol string and set operations.
L={A,B, … ,Z,a,b, … ,z}
D={0,1, … ,9}
Description meaning under represented:
LUD
LD
L4
L*
D+
L (LUD) *
solution:
LUD: a collection of all uppercase and lowercase letters and numbers
LD: the set of all symbols consisting of a letter string and a number composed of
L4: a set of strings of symbols of the four-letter
L *: ξ set and all symbol string of the alphabet
D +: all symbols of one or several strings of digits
L (LUD) *: beginning with the letter, followed by a set of all strings all symbols consisting of letters and numbers
2. grammar G (Z): Z-> aZb | ab definition of what kind of language?
solution:
Production: Z-> aZb, Z-> ab
Deduced: Z-> aZb-> aaZZbb-> aaaabbbb
Therefore language: L (G [Z]) = {aⁿbⁿ | n≥1}
3. Write grammar quaternion form materials 22 pages identifiers in example 2.2 (V N , V T , P, S).
solution:
Grammar G = (VN, NT, P, S), B is set to the identifier, L letter, D is a number.
Wherein, VN = {identifier, letters, numbers,} = {B, L, D}, VT = {a, b, c, ..., x, y, z, 0,1,2, ..., 9}
p={
<B>-><L>
<B>-><B><L>
<B>-><B><D>
<L>->a
<L>->b
...
<L>->z
<D>->0
<D>->1
...
<D>->9
}
S=<B>
4. Write the following expressions leftmost derivation, rightmost derivation.
G (E):
E=> E + T | T
T=>T * F | F
F=>（E）| i
- i*i+i
- i+i*i
- i+(i+i)
Observe different leftmost and rightmost derivation process.
solution:
i*i+i：
最左推导：E=>E+T=>T+T=>T*F+T=>F*F+T=>i*F+T=>i*i+T=>i*i+F=i*i+i
最右推导：E=>E+T=>E+F=>E+i=>T+i=>T*F+i=>T*i+i=>F*i+i=>i*i+i
i+i*i:
最左推导：E=>E+T=>T+T=>F+T=>i+T=>i+T*F=>i+F*F=>i+i*F=i+i*i
最右推导：E=>E+T=>E+T*F=>E+T*i=>E+F*i=>E+i*i=>T+i*i=>F+i*i=>i+i*i
i+(i+i):
最左推导：E=>E+T=>T+T=>F+T=>i+T=>i+F=>i+(E)=>i+(E+T)=>i+(T+T)=>i+(F+T)=>i+(i+T)=>i+(i+F)=>i+(i+i)
最右推导：E=>E+T=>E+F=>E+(E)=>E+(E+T)=>E+(E+F)=>E+(E+i)=>E+(T+i)=>E+(F+i)=>E+(i+i)=>T+(i+i)=>F+(i+i)=>i+(i+i)